Questions and Answers
What is the initial number of carbon-14 atoms in the organism at death?
How many atoms of carbon-14 will be present after 14,325 years if the initial amount was 200?
35.36
What are the properties of carbon-14? (Select all that apply)
What sensitive tool did Willard F. Libby use to date artifacts?
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Where did Willard F. Libby receive his undergraduate degree?
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Which function represents exponential decay?
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Which graph represents exponential decay?
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In order for the table to show exponential decay, what must the value of d be?
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Which statements describe the function f(x) = 3()x? (Select all that apply)
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Which function represents the given graph?
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Which graph represents the function f(x) = (3/2)^(-x)?
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What values should the doctor use for a and b in the exponential function representing bone density?
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Which statements about the bee population situation are true? (Select all that apply)
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How do the graphs of the functions f(x) = ()x and g(x) = ()x compare?
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Study Notes
Exponential Decay Functions
- Carbon-14 decay: Initial count is 500 atoms. After 11,460 years, only 125 atoms remain, leading to 25 atoms after additional years.
- Half-life of carbon-14 is approximately 5,730 years; this means after 14,325 years, 35.36 atoms will be left if starting with 200.
Properties of Carbon-14
- Functional properties and specific characteristics must be verified against provided reading.
Willard F. Libby
- Developed sensitive tools for dating artifacts, indicating precise methodologies in radiocarbon dating.
- Completed undergraduate degree at D and graduate studies leading to a professorship at D. Awarded Nobel Prize in B in 1960.
Functions and Graphs
- Functions representing exponential decay must be identified (like N(t) = N0).
- Graphs indicating exponential decay can be distinguished from those showing growth; correct representation can be found labeled D or B in examples.
Bone Density in Patients
- Doctor's function to model patient’s bone density loss at 3% annually requires initial density of 1,500 kg/mg³, and decay factor of 0.97 in function form f(x) = ab^x.
Bee Population Dynamics
- Farmer observes a population of 9,000 bees decreasing at 5% per year; implications and characteristics of the function representing this decline must be analyzed.
Graph Comparisons
- Examining relationships between graphs of exponential functions can show relationships such as reflections across axes; specifically, one function demonstrating growth while the other showcases decay.
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Description
Test your knowledge on exponential decay functions with a focus on carbon-14. This quiz covers the concept of half-life and provides examples using carbon-14 atoms in organisms. Enhance your understanding of mathematical modeling in decay processes.
